OK, welcome to the last AI1 lecture of this year.

I can see that the holidays are beckoning.

That's fine.

We're still in the logic part.

And I basically told you that we started out

with some very, very simple logic, propositional logic,

or PLNQ or so.

And we now want to graduate to a much more,

I'll probably use this, to a more expressive logic.

It's called first-order logic.

You can think of propositional logic

as kind of zeroth-order logic.

And when you hear zeroth-order logic and first-order logic,

you probably ask yourselves, is there more than 0 and 1?

And indeed, there is.

There are what is called higher-order logics.

That there's a whole tower of logics

that's much more expressive than first-order logic.

But only very few people actually use them,

even though they're extremely useful for many things.

There are indeed logics for almost anything you can imagine.

There are logics that are between first-order logic

and propositional logic.

We're going to look at those under the heading

of knowledge representation.

But there are also kind of logics on the sides.

There are logics for talking about beliefs and desires.

There are logics about having to do something, legal logic.

You ought to do this, and so on.

There are logics for that, so-called modal logics.

There are default logics, where you can basically,

we talked about Tweety, where you

can deal with exceptions, and exceptions to exceptions,

and those kind of things.

Again, very important for legal reasoning.

And all kinds of logic.

We are going to look at the big two, classical logics,

the logics that talk about true and false, essentially.

That's propositional logic.

And about infinite worlds with a lot of structure.

Those are the first-order logic.

For math, we need more.

I'll go into that in a second.

Also, for computer science, we need more.

Actually, we need less.

And I'll also come to this.

So the motivation I try to capture you with

is that we want to, even in a very small little domain

like blocks on a tabletop, we want to say things like,

all blocks are red, all blocks are on the table.